改进的同伦内点方法求解非线性规划问题

Modified Homotopy Interior Point Method to Solve Nonlinear Programming Problems

最近学者们提出了组合同伦内点法(简记为CHIP方法)去求解一类非线性规划问题。在求解凸规划问题时,与内路径跟踪算法相比,文中在没有要求对数障碍函数是严格凸的以及解集是非空有界的条件下,取得了CHIP方法的全局收敛性结果。文中对CHIP方法进行了改进并利用改进的方法去求解更大一类的非凸规划问题。数值例子表明此改进是有效的。

Recently, a combined homotopy interior point method （denoted as CHIP method for convenience） was presented to solve a class of nonlinear programming problems. For convex programming problems, compared with interior path-following methods, the authors obtained global convergence results without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. In this paper, they modify the CHIP method and use the modified one to solve a broader class of non-convex programming problems. The numerical results show that this modification is effective.